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I am currently studying for a Bachelors in Mathematics from Imperial College London, from which I am graduating in June 2024. After graduation I will continue my studies with a masters, where I intend to focus on the mathematical foundations of machine learning. I have a strong desire to conduct research in this field and am actively seeking opportunities to do this.

My interests are diverse and not pinned to a specific discipline. I get captivated by the playful nature of the abstract, and I am fascinated at the elegant solutions devised in the practical application of ideas. My attention is peaked by the theories of machine learning as they harmoniously entertain these two aspects of mathematics. I am absorbed by the application abstract concepts to structure machine learning. From my perspective there is a gap between our theoretical understanding and the observed performance of deployed machine learning models. One of my motivations is to progress the frontier of theoretical machine learning such that we can harness the full capacity of this technology and expand its capabilities in an effective and reliable manner. Currently, my interests include,

• Geometric Deep Learning,
• Category Theory for Machine Learning,
• Neural Network Generalization, and
• The Topology of Neural Networks.

However, I am eager to learn about new ideas that operate on the boundary of pure mathematics and theoretical machine learning. A subject that that I also take an interest in is AI safety. I am open to understand how some of my interests detailed above can be applied to the field of AI safety. I enjoy contemplating the philosophical conundrums encountered when discussing the impacts of AI systems. I would enjoy opportunities to have conversations on the nature of intelligence, consciousness, morality and other mysteries that arise when one takes a philosophical perspective on AI.

Academic Projects

An Investigation into Neural Network Generalization (July - August 2023)

• Imperial College London - Undergraduate Research Project
• Main Work:
  • Using Region Testing to Evaluate PAC Bounds
  • A Guide to Probably Approximately Correct Bounds for Neural Networks
    • With slight digression into reinforcement learning.
• Subsidiary Work:
  • Appealing to Gradients to Investigate Neural Network Generalization
  • The Information Theoretic Approach Taken to Investigate Neural Network Generalization
  • A Topological Perspective on Neural Network Training
  • Other Approaches for Investigating Neural Network Generalization
  • Connecting Ideas About Neural Network Generalization
  • Remarks on Neural Network Generalization

Jordan Algebras (June 2023)

• Imperial College London - Second Year Group Research Project

Reinforcement Learning Algorithm for HIV Treatment (March 2022)

• Imperial College London - Interdisciplinary Research Computing

Pseudo Random Number Generators in Python, R, and C++ (September 2022)

• Imperial College London - Undergraduate Research Project

Point Processes For Equipment Failure Simulation (June 2022)

• Imperial College London - First Year Individual Research Project

Analyzing to What Extend AI Decision Making Perpetuates Existing Social Imbalances and Injustices (December 2021)

• Imperial College London - Science and Communications Studies

Individual Projects

Artificial Intelligence Safety Fundamentals

Presentations

Using Region Tests to Evaluate PAC Bounds

• Imperial College London - Verification of Autonomous Systems Group Seminar

Aligning Pseudo-Random Number Generation in Python, R and C++

• Imperial College London - 3-Minute UROP Thesis Talk

Articles

The Prime Minister’s Mathematical Propositions (July 2023)

• Imperial College London - Faculty of Natural Sciences Blog Post

An Investigation Into Procedure Cloning

A Thought Experiment

Intelligence

Developed Material on the Imperial Maths Wiki

I am an administrator for a student-led initiative at Imperial College London. To learn more about the work we do click here.

• MATH40002 Analysis
  • Worked Solutions
• Math40003
  • Solutions to Lecture Notes Exercises
• MATH40004 Calculus with Applications
  • Quiz Solutions
• MATH40005 Probability and Statistics
  • Summary Pages
• MATH40007 Introduction to Applied Mathematics
  • Summary Pages
  • Worked Examples
• MATH50001 Real Analysis and Complex Analysis
  • Worked Solutions
• MATH50003 Linear Algebra and Numerical Analysis
  • Unseen Project Worked Solutions
  • Summary Pages
• MATH50005 Group and Rings
  • Worked Solutions
• MATH50010 Probability for Statistics
  • Summary Pages
  • Solutions to Lecture Note Exercises
• MATH50011 Statistical Modelling
  • Summary Pages
• MATH60031 Markov Processes
  • Summary Pages
• MATH60034 Algebraic Topology
  • Summary Pages
• MATH60035 Algebra 3
  • Summary Pages
• MATH60043 Statistical Theory
  • Summary Pages
• MATH60047 Stochastic Simulations
  • Summary Pages
• MATH60049 Introduction to Statistical Learning
  • Summary Pages